Is there a term for words that have a single meaning or are only used in a single context?
Solution 1:
It's a "stormy petrel." The idea, as described on the linked page, is that (for example) you never (or, at least, rarely) find a petrel that's not stormy. Similarly, "all shrift is short," and lots of other examples. One of the ones there is in fact "every skirl is of bagpipes."
Solution 2:
Closely related are fossil words, which have no meaning outside of a certain set phrase. "Bated" survives only in "bated breath", for example.
Solution 3:
There are several terms for closely related concepts:
A nonce word is a word that somebody made up for a localized purpose. Apart from fossilized words, those nonce words that caught on are probably the major part of this group.
A cranberry morpheme is a morpheme that has no meaning on its own, and exists only as part of one or a small number of words. (It's named after the "cran" of "cranberry".) A fossil word is similarly a word that is used only in a small number of phrases (but whose state is specifically due to the original meaning's obsolescence).
A hapax legomenon (of a particular corpus) is a word that appears exactly once.
Solution 4:
There is no clear word or term that conveys words that have a single meaning or are only used in a single context. The nearest match is the word unequivocal:
having only one possible meaning or interpretation.